Answer:
The coordinates of C" are (-7, 4)
Step-by-step explanation:
- If the point (x, y) rotated about the origin by angle 90° counterclockwise, then its image is (-y, x)
- If the point (x, y) translated horizontally to the left by h units, then its image is (x - h, y)
From the given figure
∵ ABCD is a trapezoid
∵ The coordinates of the ponit C are (4, 1)
∴ x = 4 and y = 1
∵ The trapezoid is rotated 90 degrees counterclockwise about the origin
→ By using the 1st rule above, change the sigh of y and switch them
∴ C' = (-y, x)
∴ C' = (-1, 4)
∵ The resulting image is translated 6 units left
→ By using the 2nd rule above subtract the x-coordinate by 6
∴ C" = (x - h, y)
∵ h = 6
∵ x = -1 and y = 4
∴ C" = (-1 - 6, 4)
∴ C" = (-7, 4)
∴ The coordinates of C" are (-7, 4)
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